The 10-year-old girl whose family successfully fought a rule preventing her from qualifying for adult lungs was in recovery after she received a lung transplant from an adult donor, according to a family statement.

Sarah Murnaghan of Newtown Square, Pa., was dying of cystic fibrosis when her family brought the Under 12 Rule, a little-known organ transplant policy, to national attention after arguing that it had been pushing Sarah to the bottom of the adult lung transplant waiting list.

The family won a court order to put Sarah on equal footing with adults on the transplant list and prompted an Organ Procurement and Transplantation Network policy change.

"Sarah got THE CALL," her mother, Janet Murnaghan, wrote on her Facebook page this morning. "She will be taken back to the O.R. in 30 minutes."

The surgery began at 11 a.m. and lasted for six hours without complications, according to a statement from the family. Sarah then entered the intensive care unit.

"We are thrilled to share that Sarah is out of surgery," they wrote. "Her doctors are very pleased with both her progress during the procedure and her prognosis for recovery."

During Sarah's surgery, Murnaghan told ABC News station WPVI that she wasn't nervous about it.

About noon, her mother wrote, "Sarah is in surgery now!"

Family spokeswoman Tracy Simon told ABCNews.com that the family expected the surgery to take several hours, but Janet Murnaghan said she wasn't worried.

"When I was nervous was [when I was] watching this kid of mine lying in this bed, and feeling like we were at the end, and not knowing if those lungs would come," she told WPVI, the ABC News station in Philadelphia. "So right now, I feel like we have a chance."

Sarah's lawyers convinced federal Judge Michael Baylson on June 5 that the Under 12 Rule was discriminatory, prompting a temporary restraining order against Health and Human Services Secretary Kathleen Sebelius to prevent her from enforcing it for Sarah.

Baylson's ruling forced OPTN to create a second database entry for Sarah with a fake birthday to trick the organ transplant system into thinking she was 12. The following day, another child in Sarah's hospital, Javier Acosta, 11, won the same reprieve.

The Organ Procurement and Transplantation Network voted to keep the so-called Under 12 Rule, but it created a mechanism that would allow doctors to request exceptions for their pediatric patients. A national lung review board would then approve these children for transplant consideration as adults case by case.

Last week, a hearing was scheduled for June 14, at which point a judge could have ruled to reinstate the Under 12 Rule for Sarah -- at least until the OPTN's lung review board could determine whether her case warranted an exception to the rule. If she hadn't received lungs by then, it wasn't clear whether the duplicate organ candidate record would be deleted.

"I cannot comment on any legal aspects of the case, but I will say that I am very happy right now, and I hope that the surgery is successful," Sarah's lawyer, Steve Harvey, said in a statement.

Sarah had been living at the Children's Hospital of Philadelphia for more than two months and was intubated on June 8. Her mother notified Sarah's Facebook community on Sunday that Sarah was terrified when she wasn't sedated because of the "thick secretions coming out of her lungs and into her throat," causing her to choke and panic.

"It's been terrifying and we have felt so helpless," Murnaghan wrote. "At one point last night I thought we would lose her. I have never felt such sheer panic and terror in my life."

Sarah was born with cystic fibrosis, a genetic condition that affects cells that produce mucus, sweat and digestive fluid. Patients typically suffer so much lung damage that they often go into respiratory failure, which is why Sarah needs a lung transplant to survive.

After spending 18 months on the transplant waiting list, her condition rapidly deteriorated in late May, and her family expected her to be bumped to the top of the adult waiting list because of the severity of her condition, Sarah's aunt, Sarah Ruddock, told ABCNews.com.

"A week went by with nothing, no offers," Ruddock said. "They said, 'Well, you're not at the front of the line. It goes to all adults, and if all the adults turn them down, the lungs go to the kids.'"

Here's how the Under 12 Rule -- which is more like a series of rules -- actually works:

Lung transplant candidates older than 12 are assigned a lung allocation score, or LAS, based on a complex mathematical formula that includes the patient's age and size. For transplant patients younger than 12 -- of which there are 20 nationally compared with about 1,600 adults -- the LAS is not used. Instead, patients are broken into "priority 1" and "priority 2." It's this difference that has been called discriminatory in court.

Children get priority for lungs donated from children younger than 12, but they have to wait for children between 12 and 17 to decline lungs donated from 12- to 17-year-olds before they get a chance at them. Lungs donated by anyone older than 18 are offered to all candidates older than 12, depending on their LAS. Only if all local matching candidates 12 and older decline the adult lungs can they be offered to children within 500 miles of the hospital where the lungs were harvested.

Sarah's lung transplant from an adult donor will be the 11th of its kind since 1987. The last transplant from a donor older than 18 to a child younger than 12 took place a few months ago, according to an OPTN spokesperson. The one before that happened in 2006, when the Under 12 Rule was new.

Because of the court ruling, Sarah has had two transplant database records -- one with her actual birthday and one with a fake 12-year-old birthday -- since last week so she can be considered for child lungs based on her priority level and adult lungs based on her LAS.

Sarah, who dreams of being a singer and a veterinarian, told her parents she wanted to fight for her life but did not know how dire her situation was.

However, Ruddock said she probably knew. Sarah lost her hearing a few weeks ago as a side effect of one of the antibiotics keeping her alive. At bedtime, she began asking her parents if she'd wake up.

At the end of May, Sarah's siblings and cousins gathered to say goodbye to Sarah even though their parents didn't say what was going on, Ruddock said. Doctors told the family that they weren't sure Sarah would survive Memorial Day weekend, but she pulled through.

"She was the little leader in our family. She would always get the little kids to put on a play for us," Ruddock said. "She's a bit of a pistol with a good personality to survive. She's not meek. She's a tough kid."